Lesson 2-7 Proving Segment Relationships. Ohio Content Standards:

Lesson 2-7Lesson 2-7Proving Segment Proving Segment

RelationshipsRelationships

Ohio Content Standards:Ohio Content Standards:

Ohio Content Standards:Ohio Content Standards:

Establish the validity of conjectures Establish the validity of conjectures about geometric objects, their about geometric objects, their

properties and relationships by properties and relationships by counter-example, inductive and counter-example, inductive and

deductive reasoning, and critiquing deductive reasoning, and critiquing arguments made by others.arguments made by others.

Ohio Content Standards:Ohio Content Standards:

Make and test conjectures about Make and test conjectures about characteristics and properties (e.g., characteristics and properties (e.g.,

sides, angles, symmetry) of two-sides, angles, symmetry) of two-dimensional figures and three-dimensional figures and three-

dimensional objects.dimensional objects.

Ohio Content Standards:Ohio Content Standards:

Make, test and establish the validity of Make, test and establish the validity of conjectures about geometric conjectures about geometric

properties and relationships using properties and relationships using counterexample, inductive and counterexample, inductive and

deductive reasoning, and paragraph deductive reasoning, and paragraph or two-column proof.or two-column proof.

Postulate 2.8Postulate 2.8Ruler PostulateRuler Postulate

Postulate 2.8Postulate 2.8Ruler PostulateRuler Postulate

The points on any line or line The points on any line or line segment can be paired with real segment can be paired with real numbers so that, given any two numbers so that, given any two

points points AA and and BB on a line, on a line, AA corresponds to zero, and corresponds to zero, and BB

corresponds to a positive real corresponds to a positive real number.number.

Postulate 2.9Postulate 2.9Segment Addition Segment Addition

PostulatePostulate

Postulate 2.9Postulate 2.9Segment Addition Segment Addition

PostulatePostulateIf If BB is between is between AA and and CC, ,

then then AB + BC = ACAB + BC = AC..

Postulate 2.9Postulate 2.9Segment Addition Segment Addition

PostulatePostulateIf If BB is between is between AA and and CC, ,

then then AB + BC = ACAB + BC = AC..

If If AB + BC = AC,AB + BC = AC,

then then B B is between is between A and C.A and C.

Prove the following.Prove the following.

Given: Given: PR = QSPR = QSProve: Prove: PQ = RSPQ = RS

P Q R S

Theorem 2.2Theorem 2.2Segment CongruenceSegment Congruence

Theorem 2.2Theorem 2.2Segment CongruenceSegment Congruence

Congruence of segments is reflexive, Congruence of segments is reflexive, symmetric, and transitive.symmetric, and transitive.

..

Theorem 2.2Theorem 2.2Segment CongruenceSegment Congruence

Congruence of segments is reflexive, Congruence of segments is reflexive, symmetric, and transitive.symmetric, and transitive.

Reflexive PropertyReflexive Property

AB ABAB AB..

Theorem 2.2Theorem 2.2Segment CongruenceSegment Congruence

Congruence of segments is reflexive, Congruence of segments is reflexive, symmetric, and transitive.symmetric, and transitive.

Symmetric PropertySymmetric Property

If If AB CDAB CD, then , then CD AB.CD AB...

Theorem 2.2Theorem 2.2Segment CongruenceSegment Congruence

Congruence of segments is reflexive, Congruence of segments is reflexive, symmetric, and transitive.symmetric, and transitive.

Transitive PropertyTransitive Property

If If AB CDAB CD, and , and CD EF, CD EF,

then then AB EF.AB EF...

Prove the following.Prove the following.

Given:Given: WY = YZWY = YZYZ XZYZ XZXZ WXXZ WX

Prove:Prove: WX WYWX WY

Z

W X

Y

3 cm

3 cm

Assignment:

Pgs. 104 - 106 12-20 all, 31-38 all